Quandaries and Queries 

Name: Phillip
Question:
I am interested in Sacred Geometry and would be grateful if you could show me a geometrical proof for the following. Hi Phillip, An easy proof depends on knowing that the golden section is the positive number that satisfies the equation x^{2} = x+1. One also must know If you extend MN in both directions to meet the circle, by symmetry one sees that the distance from M to the circle equals the distance from N to the circle. We choose that distance to be our unit length. We now have two chords through M; one is divided by M into lengths 1 and x+1 while the other has AM = MB = x. Using theorem (*) we get x*x = x+1, so x:1 must be the golden ratio. Chris 

